Wolfram Language & System 11.0 (2016)|Legacy Documentation

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a.b.c or Dot[a,b,c]
gives products of vectors, matrices, and tensors.


  • a.b gives an explicit result when a and b are lists with appropriate dimensions. It contracts the last index in a with the first index in b.
  • Various applications of Dot:
  • {a1,a2}.{b1,b2}scalar product of vectors
    product of a vector and a matrix
    product of a matrix and a vector
    product of two matrices
  • The result of applying Dot to two tensors and is the tensor . Applying Dot to a rank tensor and a rank tensor gives a rank tensor. »
  • Dot can be used on SparseArray objects, returning a SparseArray object when possible. »
  • When its arguments are not lists or sparse arrays, Dot remains unevaluated. It has the attribute Flat.
Introduced in 1988
| Updated in 2003